Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.*;
import java.awt.geom.*;
import java.io.*;
import java.math.*;

public class Main
{

  public static void main(String[] args) throws Exception
  {
    long startTime = System.nanoTime();
    int n=in.nextInt();
    int m=in.nextInt();
    int [][] grid = new int[n+1][m+1];
    StringBuilder res=new StringBuilder();
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=m;j++)
        {
            grid[i][j]=in.nextInt();
        }
    }
    int ans=0;
    if(n<=m)
    {
    for(int i=1;i<=n;i++)
    {
        while(getRow(grid,i,m))
        {
            res.append("row "+i+"\n");
            ans++;
            updateRow(grid,i,m);
        }
    }
    for(int i=1;i<=m;i++)
    {
        while(getCol(grid,i,n))
        {
            res.append("col "+i+"\n");
            ans++;
            updateCol(grid,i,n);
        }
    }
    }
    else
    {
    for(int i=1;i<=m;i++)
    {
        while(getCol(grid,i,n))
        {
            res.append("col "+i+"\n");
            ans++;
            updateCol(grid,i,n);
        }
    }
    for(int i=1;i<=n;i++)
    {
        while(getRow(grid,i,m))
        {
            res.append("row "+i+"\n");
            ans++;
            updateRow(grid,i,m);
        }
    }  
    }
    if(ans==0 && isValid(grid,n,m))
    {
    out.println(ans);
    }
    else if(ans>0 && isValid(grid,n,m))
    {
    out.println(ans);
    out.print(res);
    }
    else   
    {
    out.println("-1");  
    }
    long endTime = System.nanoTime();
    err.println("Execution Time : +" + (endTime-startTime)/1000000 + " ms");
    exit(0);
  }





  static boolean getRow(int [][] grid,int r,int m)
  {
    int min=grid[r][1];
        for(int j=1;j<=m;j++)
            {
                if(grid[r][j]<min)
                {
                    min=grid[r][j];
                }
            }
    return min!=0;
  }

  static boolean isValid(int [][] grid,int n,int m)
  {
    for(int i=1;i<=n;i++)
    {
        for(int j=1;j<=m;j++)
        {
            if(grid[i][j]>0)
                return false;
        }
    }
    return true;
  }

  static void updateRow(int [][] grid,int r,int m)
  {
        for(int j=1;j<=m;j++)
            {
                grid[r][j]--;
            }
  }

  static void updateCol(int [][] grid,int c,int n)
  {
        for(int j=1;j<=n;j++)
            {
                grid[j][c]--;
            }
  }

  static boolean getCol(int [][] grid,int c,int n)
  {
    int min=grid[1][c];
        for(int j=1;j<=n;j++)
            {
                if(grid[j][c]<min)
                {
                    min=grid[j][c];
                }
            }
    return min!=0;
  }

  static class InputReader
  {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble(){
           return Double.parseDouble(next());
        }
    }

    static void exit(int a)
    {
      out.close();
      err.close();
      System.exit(a);
    }

    static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static OutputStream errStream = System.err;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);
    static PrintWriter err = new PrintWriter(errStream);
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

}